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Foundations
 Axioms & Definitions
 Contradiction & Game semantics & True induction
 Circularity in mathematics & 'Paradoxes' resolved
 Building blocks & Incompleteness theorems
 Logic texts
Natural deduction
Rigour + Intuition
 Naturals
 Reals & Real exponentiation & $\cos,\sin$ & $\exp(iπ)+1=0$
 General differentiation & applications
 Matrix multiplication
Beautiful stuff
Puzzles:
Finite difference:
Asymptotic expansion:
 ktimesdifferentiable function
 Central difference formulae
 NewtonRaphson convergence criteria
 Systematic computation of limits
Smoothing:
 To prove AMGM & Jensen's inequality
 Maximum area of polygon given perimeter
 Maximum expression value using brackets
Multidimensional analysis:
 Multidimensional IVT, which proves:
 Poincaré–Miranda theorem
 Ham sandwich theorem [consider all hyperplanes that bisect one piece]
Inversion:
Common oversights
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Yearling
× 9Apr 27
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CommentatorAug 27, 2022

CriticNov 22, 2015

SupporterDec 1, 2015
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